Very sadly, I do not have an answer to today's challenge and to be completely honest, I am ok with that. I think the notion of independence or strong opinion is variable, in that it can change depending on a given topic.
For instance, some of your friends and family may have a different opinion of a certain good or service than you; however, when it comes to strong beliefs ... I think it's very hard to have one that will be distinctly different to what your close friends and family believe.
In fact, it almost seems oxymoronic to have a strong belief that is not shared by your close friends or family. The very fact that they are your close friends and family would generally mean that they share the same strong beliefs as you do.
I believe in the notion of strongly believing in something and to me it should not necessarily matter who else believes in it, so long as you do. In most cases though, if your belief is strong enough ... you will typically find you are not alone.